We further account for particle rotation as well as steric
interactions, and couple MT motion with a background flow to study the
effect of long-range hydrodynamic interactions absent in the BD-MC
simulations through a continuum polar fluid model
[1]}, [2]}, [3]}, [4]}, [5]}, [6]}. Since in
the Sanchez et al. experiments [7]} the active
material is confined to an interface between oil and water, we assume
a thin layer of suspension immersed in the bulk viscous liquid, and
close the system by solving the hydrodynamic coupling between the
surface flow \({\bf U}\)  and external fluid motions through a
velocity-stress relation in Fourier space: \({\hat{{\bf U}}} = \frac{i}{2}({\bf I}- {\hat{{\bf k}}}{\hat{{\bf k}}})({\hat{\mathbf {\Sigma }}}^e{\hat{{\bf k}}})\) , where \({\bf {\hat{k}}} = {\bf {k}}/k\)  is the normalized 2D wave-vector [6]}.
